1) dual weighted Markov branching process
对偶加权分支过程
2) pre-dual process
对偶分支过程
1.
In this paper,the basic properties regarding stochastic monotonicity,duality and FRR property on the q-matrix and the minimal transition function for the pre-dual process are discussed.
讨论了分支过程的前对偶过程(以下称对偶分支过程)的单调性、Feller-Reuter-Riley(简称FRR)性和常返性等基本性质,同时给出了对偶分支过程最小Q-函数为FRR和遍历的判别条件。
4) dual branching process with immigration
带迁移对偶分支过程
1.
This paper describes a dual branching model,which is called "dual branching process with immigration"(DBPI),that accounts for the effect of immigration,establishes that there is a unique DBPI,and derives necessary and sufficient conditions for it to be positive recurrent.
并且给出了刻画带迁移对偶分支过程常返性的充要条件及正常返性的必要条件。
5) dual processes
对偶过程
1.
We discuss the time changes of dual processes and the associated quasi-regulal Dirichlet form, and prove that under certain conditions the dual-invariance of the processes and the quasi-regular invariance of the Dirichlet form hold under this time change.
证明了相伴于拟正则狄氏型的对偶过程关于对偶可加泛函的时间变换，在一定条件下仍为对偶过程，且它们相伴的狄氏型仍为拟正则的。
6) branching process
分支过程
1.
The underlying model is a two-type branching process.
根据流行病发生的特点,一般其发生的时刻、感染者的人数等因素不易直接得出,但是在某一时间内被发现患病者的人数是可以知道的,从而可以根据该已知数据,利用分支过程构建一个新的模型,利用该方法,可以预测将来流行病的发展情况,从而可以采取相应措施来控制疾病。
2.
By means of probability generating function,for the bisexual GaltonWatson branching process with a certain mating function always taken the number of females as its value,the necessary and sufficient condition of the process extinction with probability 1 was given,and the expressions of expectation and variance of the process were obtained.
利用概率母函数,对带有取值恒等于雌性数目的配对函数的两性Galton Watson分支过程,给出了其以概率1灭绝的充分必要条件,并求得了相应的数学期望与方差的表达式。
3.
The method mentioned can be applied to a number of old and new cases of branching processes.
此种处理方法为处理大量旧的与新的分支过程提供了一个一致逼近的途径。
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